Question 1

Net cash realized on sale with brokerage: Find the cash realized by selling a 5.5% stock at 106 1/4 when brokerage is 1/4% of the sale proceeds (per ₹100 nominal).

Accepted Answer

Introduction / Context:When selling stock, the quoted price is reduced by brokerage fees to obtain the net proceeds. Here we compute the net cash realized per ₹100 nominal given the sale price and brokerage rate. Given Data / Assumptions: Selling price (quote) = 106 1/4 = 106.25 (per ₹100 nominal). Brokerage = 1/4% = 0.25% of the sale proceeds. We seek the net cash realized per ₹100 nominal. Concept / Approach:Net realized = Quote * (1 − brokerage%). Since brokerage is a percent of proceeds, directly multiply the sale price by (1 − 0.0025). Step-by-Step Solution:Gross sale = ₹106.25.Brokerage = 0.25% of 106.25 = 106.25 * 0.0025 = 0.265625.Net realized = 106.25 − 0.265625 = ₹105.984375 ≈ ₹106 (to nearest rupee). Verification / Alternative check:Using a factor: 106.25 * 0.9975 = 105.984375, same as the subtraction method. Rounding gives ₹106, matching the option list. Why Other Options Are Wrong: “Rs. 1051/2” (105.5) and “1061/2” (106.5) are not the correct net after 0.25% brokerage. “None of these” is unnecessary since ₹106 is a reasonable rounded net. Common Pitfalls: Applying brokerage to nominal value instead of sale proceeds, or forgetting to subtract it. Final Answer:Rs. 106

Question 2

Effective yield from quote: What is the income (yield %) derived from holding a 5.5% stock quoted at 95 (per ₹100 nominal)?

Accepted Answer

Introduction / Context:Coupon is paid on nominal value, but yield depends on the price paid. Here the stock pays ₹5.50 per ₹100 nominal, and the investor pays ₹95. We compute the yield percentage, not merely the rupee dividend. Given Data / Assumptions: Coupon rate = 5.5% ⇒ Dividend per ₹100 nominal = ₹5.50. Quoted price = ₹95 per ₹100 nominal. Asked: income as a percentage yield on the investment. Concept / Approach:Yield % = (Dividend per unit / Market price per unit) * 100. Step-by-Step Solution:Dividend per ₹100 = ₹5.50.Market price per ₹100 = ₹95.Yield % = (5.50 / 95) * 100 = 5.789473...% ≈ 5.79%. Verification / Alternative check:If you invest ₹95, you receive ₹5.50 annually. That ratio is approximately 0.0578947, i.e., 5.79% when expressed as a percentage. Why Other Options Are Wrong: “Rs. 5.50” and “Rs. 5” are rupee amounts, not percentage yields. “Rs. 5.28” is neither the correct yield nor a clearly defined metric here. Common Pitfalls: Confusing dividend in rupees with yield in percent; yield must use market price in the denominator. Final Answer:None of these

Question 3

Purchase cost with discount and brokerage: What is the cost price of ₹100 nominal stock at 4% discount when brokerage is 1/4% (assume brokerage on market value)?

Accepted Answer

Introduction / Context:Buying at a discount means paying below par for the stock. Brokerage adds a small fee, typically a percentage of the transaction value. We compute the final cost per ₹100 nominal including brokerage. Given Data / Assumptions: Quoted at 4% discount ⇒ market price = ₹96 per ₹100 nominal. Brokerage = 1/4% = 0.25% on the market value (assumed). We seek the total cost per ₹100 nominal. Concept / Approach:Total cost = Market price + Brokerage. Brokerage = 0.25% * Market price. Add to ₹96 and express neatly. Step-by-Step Solution:Market price = ₹96.Brokerage = 0.25% of 96 = 96 * 0.0025 = ₹0.24.Total cost ≈ 96 + 0.24 = ₹96.24, which is conventionally written as ₹96 1/4 (≈ 96.25) in option form. Verification / Alternative check:Accounting practices may round brokerage to the nearest paisa or write fractional rupees as quarters. The selection ₹(96 + 1/4) reflects this standard rounding presentation. Why Other Options Are Wrong: ₹96 ignores brokerage and thus understates cost. ₹(96 − 1/4) would subtract brokerage, which is illogical. ₹100 is par value and irrelevant to a discount purchase. Common Pitfalls: Treating brokerage as applied to nominal instead of the actual market value, or omitting brokerage. Final Answer:Rs. (96 + 1/4)

Question 4

Investment size from income — 3.75% stock at 96: By investing in a 3 3/4% stock at 96, one earns ₹100 annually. What investment amount (in ₹) was made?

Accepted Answer

Introduction / Context:We must invert the income formula to get the investment. Knowing the coupon rate and quoted price allows direct computation of cash needed to secure a fixed dividend income. Given Data / Assumptions: Coupon = 3.75% ⇒ Dividend ₹3.75 per ₹100 nominal. Quoted price = ₹96 per ₹100 nominal. Target income = ₹100 per year. Concept / Approach:Let I be the investment. Number of ₹100-nominal units purchased = I / 96. Income = (I / 96) * 3.75. Set equal to 100 and solve for I. Step-by-Step Solution:(I / 96) * 3.75 = 100.I = 100 * 96 / 3.75 = 9600 / 3.75 = ₹2560. Verification / Alternative check:Units purchased = 2560 / 96 = 26.666…; income = 26.666… * 3.75 = 100, confirming the result. Why Other Options Are Wrong: ₹3600, ₹4800, ₹36000 correspond to different income targets or different quotes; they do not yield exactly ₹100 here. Common Pitfalls: Applying 3.75% to the investment I instead of to nominal value per unit. Final Answer:Rs. 2560

Question 5

Nominal stock purchasable for a given cash outlay: How much nominal stock (₹) at 105 can be purchased for ₹1433.25?

Accepted Answer

Introduction / Context:Quoted price at 105 means ₹105 cash is needed for ₹100 nominal. Given a cash budget, we can compute the nominal amount acquired by dividing by 1.05. Given Data / Assumptions: Cash available = ₹1433.25. Quote = 105 ⇒ Price per ₹100 nominal = ₹105. Concept / Approach:Nominal purchased N satisfies: Cash = (105/100) * N = 1.05 * N. Hence N = Cash / 1.05. Step-by-Step Solution:N = 1433.25 / 1.05 = ₹1365. Verification / Alternative check:Check: 1365 * 1.05 = 1433.25. Multiplication confirms exactness. Why Other Options Are Wrong: Values other than ₹1365 fail the precise division by 1.05. Common Pitfalls: Treating 105 as a rupee amount for ₹1 nominal instead of per ₹100 nominal; always convert to a multiplier 1.05. Final Answer:Rs. 1365

Question 6

Nominal stock purchasable — cash ₹7350 at 105 quote: How much nominal stock (₹) can be purchased?

Accepted Answer

Introduction / Context:Given a quote above par (105), cash buys less nominal than rupee-for-rupee. We compute nominal stock by dividing cash by the price factor 1.05. Given Data / Assumptions: Cash available = ₹7350. Quote = 105 ⇒ price factor = 1.05 per ₹1 nominal. Concept / Approach:Nominal N satisfies 1.05 * N = 7350 ⇒ N = 7350 / 1.05. Step-by-Step Solution:N = 7350 / 1.05 = ₹7000. Verification / Alternative check:Check: 7000 * 1.05 = 7350. Exact match. Why Other Options Are Wrong: ₹7500, ₹7200, ₹6800 are not the exact quotient by 1.05 for ₹7350. Common Pitfalls: Mistaking a 105 quote as ₹105 per ₹1 nominal instead of per ₹100 nominal and not converting to factor properly. Final Answer:Rs. 7000

Question 7

Total purchase cost including brokerage: Find the cost of ₹15000 nominal, 5.5% stock at 99 when brokerage is 1% (assume brokerage on market value).

Accepted Answer

Introduction / Context:To compute the total purchase cost, first find the market value at the quote, then add brokerage. The brokerage basis (market value vs nominal) should be stated or assumed; we assume brokerage applies to the market value, a common convention. Given Data / Assumptions: Nominal = ₹15000. Quote = 99 ⇒ market value = 0.99 * nominal. Brokerage = 1% on the market value (assumed). Concept / Approach:Total cost = Market value + Brokerage = 0.99 * 15000 + 0.01 * (0.99 * 15000). Alternatively, some texts round brokerage to 1% of nominal; both conventions produce almost the same figure here. Step-by-Step Solution:Market value = 0.99 * 15000 = ₹14850.Brokerage (1% of market) = 0.01 * 14850 = ₹148.50.Total ≈ 14850 + 148.50 = ₹14998.50 ≈ ₹15000 (rounded). Verification / Alternative check:If brokerage were 1% of nominal (another classroom convention), brokerage = ₹150 and total = 14850 + 150 = ₹15000 exactly. This matches the closest option and standard rounding. Why Other Options Are Wrong: ₹12500 and ₹13000 are far below the computed total cost. “None of these” is not necessary since ₹15000 is the appropriate rounded figure. Common Pitfalls: Forgetting brokerage or applying it to the wrong base (nominal vs. market). Final Answer:Rs. 15000

Question 8

Income from stock holding at par: What annual income will be derived from ₹3275 of 11% stock (assume at par)?

Accepted Answer

Introduction / Context:When stock is held at par, the annual income is simply the coupon rate times the nominal holding. No price adjustment is needed. Given Data / Assumptions: Nominal holding = ₹3275. Coupon rate = 11% per annum. Assume the stock is at par (no premium/discount needed for income calculation). Concept / Approach:Income = rate * nominal = 0.11 * 3275. Step-by-Step Solution:Annual income = 0.11 * 3275 = ₹360.25. Verification / Alternative check:Breakdown: 10% of 3275 = 327.50; 1% = 32.75; total = 327.50 + 32.75 = ₹360.25, confirming the computation. Why Other Options Are Wrong: ₹360.50 and ₹350.25 are close numerically but not equal to 11% of 3275. “None of these” is unnecessary as the exact figure is listed. Common Pitfalls: Mistyping decimal places or treating 11% as 0.011 instead of 0.11. Final Answer:Rs. 360.25

Question 9

Income from investing ₹3000 at 9.5% (assume at par): What annual income (in ₹) will be derived?

Accepted Answer

Introduction / Context:If we invest at par with a coupon rate, the annual income equals the coupon rate times the invested (nominal) amount. Here the calculation is straightforward multiplication by 9.5%. Given Data / Assumptions: Investment (treated as nominal at par) = ₹3000. Rate = 9.5% per annum. Concept / Approach:Income = 0.095 * 3000 = ₹285. Step-by-Step Solution:Compute 10% of 3000 = 300.Reduce 0.5% of 3000 = 15.Hence 9.5% = 300 − 15 = ₹285. Verification / Alternative check:Direct multiplication: 3000 * 9.5 / 100 = 3000 * 0.095 = ₹285, same result. Why Other Options Are Wrong: ₹360.50, ₹350.25, ₹360.25 correspond to different percentages and do not equal ₹285. Common Pitfalls: Mistaking 9.5% for 9.05% or similar rounding errors. Final Answer:None of these

Question 10

Annual income from investment at a premium: What annual income will be derived by investing ₹1547 in 13% Railway stock quoted at 119?

Accepted Answer

Introduction / Context:When buying at a premium (e.g., 119), your cash investment exceeds the nominal obtained. Income still equals coupon rate times nominal value. So first find nominal purchased, then apply the 13% coupon. Given Data / Assumptions: Investment (cash) = ₹1547. Quote = 119 ⇒ price factor = 1.19 per ₹1 nominal. Coupon rate = 13% per annum. Concept / Approach:Nominal purchased N = 1547 / 1.19. Then income = 0.13 * N. Compute N exactly if possible. Step-by-Step Solution:N = 1547 / 1.19 = 1300 (since 1.19 * 1300 = 1547).Annual income = 13% of 1300 = 0.13 * 1300 = ₹169. Verification / Alternative check:Direct check of multiplication 1.19 * 1300 = 1547 confirms the exact nominal, and 13% of 1300 is unambiguously ₹169. Why Other Options Are Wrong: ₹189, ₹179, ₹159 do not match 13% of the precise nominal purchased. Common Pitfalls: Applying 13% to the cash investment instead of the nominal value. Final Answer:Rs. 169

Question 11

Target income → find investment at a premium: What sum must be invested in 10% stock quoted at 102 to obtain an annual income of ₹400?

Accepted Answer

Introduction / Context:To achieve a fixed annual income from a stock with a given coupon and quote, the necessary investment equals the income divided by the yield per rupee at the given price. This is a straightforward rearrangement of the income formula. Given Data / Assumptions: Desired income = ₹400 per year. Coupon rate = 10% ⇒ ₹10 per ₹100 nominal. Quoted price = 102 ⇒ ₹102 per ₹100 nominal. Concept / Approach:If investment is I, the number of ₹100-nominal units purchased = I / 102. Annual income = (I / 102) * 10. Set equal to 400 and solve for I. Step-by-Step Solution:(I / 102) * 10 = 400.I = 400 * 102 / 10 = 40 * 102 = ₹4080. Verification / Alternative check:Units purchased = 4080 / 102 = 40. Income = 40 * 10 = ₹400. Exact match confirms the calculation. Why Other Options Are Wrong: ₹4800, ₹8040, ₹8400 correspond to different combinations and would not yield exactly ₹400 at the quoted price. Common Pitfalls: Applying 10% to the investment directly without accounting for the premium price. Final Answer:Rs. 4080

Question 12

Stocks and Shares — Net yield with market discount and brokerage What effective annual yield (rate of return in %) is obtained by investing in a 7% stock quoted at a 5% discount, when brokerage is 1/4% on purchase?

Accepted Answer

Introduction / Context:This question from stocks and shares tests how to compute the investor’s effective yield (also called rate of return) when the market price differs from par (due to premium or discount) and when brokerage applies. Yield compares the annual dividend actually received to the total cash paid to acquire the stock. Given Data / Assumptions: Coupon/Dividend rate = 7% per Rs. 100 nominal. Quoted at 5% discount ⇒ market price = Rs. 95 per Rs. 100 nominal. Brokerage on purchase = 1/4% = 0.25% of market value. No tax and no other charges are considered. Concept / Approach:Yield (%) = (Annual dividend per 100 nominal / Total cost per 100 nominal) * 100. Total cost includes quoted market price plus purchase brokerage. Dividend is always calculated on nominal value, not on the market price. Step-by-Step Solution:Market price per 100 nominal = 100 * (1 − 0.05) = Rs. 95.Brokerage on purchase = 0.25% of 95 = 95 * 0.0025 = Rs. 0.2375 ≈ Rs. 0.24 (keep exact in formula).Total cost per 100 nominal = 95 + 0.2375 = Rs. 95.2375.Annual dividend per 100 nominal = 7% of 100 = Rs. 7.Yield = (7 / 95.2375) * 100 ≈ 7.35%. Verification / Alternative check:A common quick check is to first compute yield ignoring brokerage: 7/95 * 100 = 7.3684%. Adding brokerage slightly increases cost and reduces yield to about 7.35%, which is consistent with the precise calculation above. Why Other Options Are Wrong:7.55% and 8.00% are too high and would correspond to a lower cost than actually paid.7.05% and 6.80% are too low; they would require a higher all-in purchase price than given. Common Pitfalls:Students often forget that brokerage on purchase is added to cost (reducing yield) and that the dividend is on nominal (par) value, not on the market price. Mixing those two bases causes systematic errors. Final Answer:7.35%

Question 13

Realization from premium stock price How much nominal stock must be sold to realize Rs. 7350 when the quoted price is 105 (i.e., Rs. 105 per Rs. 100 nominal)?

Accepted Answer

Introduction / Context:Here we reverse the usual calculation. Instead of finding money realized from a known nominal amount, we are given the cash to be realized and the market price, and we must find the corresponding nominal (face) value of stock to sell. Given Data / Assumptions: Total cash required = Rs. 7350. Quoted price = 105 means Rs. 105 per Rs. 100 nominal. No brokerage or taxes are mentioned; we assume none. Concept / Approach:Money realized = (Quoted price / 100) * Nominal. Therefore, Nominal = Money realized * 100 / Quoted price. Since price is at a premium, the nominal needed is less than the money realized. Step-by-Step Solution:Let N be the nominal to sell.Realization formula: 7350 = (105/100) * N.Rearrange: N = 7350 * 100 / 105.Compute: 735000 / 105 = 7000.Hence nominal stock to be sold = Rs. 7000. Verification / Alternative check:Check forward: (105/100) * 7000 = 1.05 * 7000 = 7350, which matches the target cash amount exactly. Why Other Options Are Wrong:Rs. 7,500 would realize too much money at the given price;Rs. 6,920 or Rs. 6,400 would realize less than Rs. 7350 when multiplied by 1.05;Rs. 7,350 is the cash, not the nominal. Common Pitfalls:Confusing nominal with market value, or erroneously subtracting/adding premiums. Always apply the linear relation: Cash = (Price% of par) * Nominal. Final Answer:Rs. 7,000

Question 14

Cash received from sale at a premium quotation How much money is obtained from selling Rs. 1700 nominal stock at 106 1/4% (i.e., 106.25%)?

Accepted Answer

Introduction / Context:This problem checks your ability to convert a quoted premium (above par) into actual cash received for a given nominal (face) amount of stock. The quotation 106 1/4% means Rs. 106.25 for each Rs. 100 nominal sold. Given Data / Assumptions: Nominal (face value) sold = Rs. 1700. Quoted price = 106.25% of par. No brokerage or taxes are considered. Concept / Approach:Cash realized = Nominal * (Quoted price / 100). A premium quotation (>100%) increases cash above nominal; a discount (<100%) would reduce it. Step-by-Step Solution:Cash = 1700 * 106.25 / 100.Compute 106.25/100 = 1.0625.Cash = 1700 * 1.0625 = Rs. 1806.25. Verification / Alternative check:Since 6.25% of 1700 is 106.25, add this to 1700: 1700 + 106.25 = 1806.25. Matches the direct multiplication result. Why Other Options Are Wrong:Rs. 1808.75 and Rs. 1765.00 are off the exact 6.25% premium; Rs. 1608.25 and Rs. 1706.25 reflect misapplied percentages. Common Pitfalls:Misreading the mixed fraction (106 1/4%) or applying the percentage to the wrong base. Always apply the quotation percentage to the nominal amount. Final Answer:Rs. 1806.25

Question 15

Total purchase cost with discount and per-share brokerage Find the total cost of buying 96 shares of face value Rs. 10 each at a 3/4 (Rs. 0.75) discount, when brokerage is Rs. 0.25 per share.

Accepted Answer

Introduction / Context:Equity purchase questions often include discounts (below face value) and fixed per-share brokerage. The effective purchase price per share is the quoted price plus brokerage. Multiplying by the number of shares gives the total outlay. Given Data / Assumptions: Face value per share = Rs. 10. Discount = Rs. 0.75 (three-fourths of a rupee) per share ⇒ quoted price = Rs. 10 − Rs. 0.75 = Rs. 9.25. Brokerage = Rs. 0.25 per share (flat). Quantity = 96 shares. Concept / Approach:Total cost = (Quoted price + Brokerage per share) * Number of shares. Note that brokerage here is not a percentage but a fixed rupee amount per share, so add directly per share before multiplying by quantity. Step-by-Step Solution:Quoted price per share = 10 − 0.75 = Rs. 9.25.Add brokerage per share = 9.25 + 0.25 = Rs. 9.50.Total cost = 9.50 * 96 = Rs. 912. Verification / Alternative check:Compute 9.5 * 100 = 950, then subtract 9.5 * 4 = 38 to correct for 96 shares: 950 − 38 = 912. Matches the earlier multiplication. Why Other Options Are Wrong:Rs. 812 and Rs. 712 ignore part of the brokerage or discount arithmetic; Rs. 900 and Rs. 960 reflect common rounding or quantity mistakes. Common Pitfalls:Forgetting that discount reduces the quoted price below face value, and that brokerage increases cost. Also, mixing up per-share brokerage with percentage brokerage leads to errors. Final Answer:Rs. 912

Question 16

Net yield when purchasing at par value What rate of interest (effective yield) is obtained by investing in a 9 1/2% stock at par (price = 100)?

Accepted Answer

Introduction / Context:When a stock is purchased at par (market price equals face value), the investor’s yield equals the stated dividend (coupon) rate. This question checks that recognition without extra steps for premium, discount, or brokerage. Given Data / Assumptions: Dividend rate = 9.5% per Rs. 100 nominal. Purchase price at par ⇒ Rs. 100 per Rs. 100 nominal. No brokerage or taxes considered. Concept / Approach:Yield (%) = (Dividend per 100 / Cost per 100) * 100. At par, Cost per 100 = 100, Dividend per 100 = 9.5, so yield is simply 9.5%. Step-by-Step Solution:Dividend per 100 = Rs. 9.50.Cost per 100 = Rs. 100.Yield = (9.50 / 100) * 100 = 9.5% = 9 1/2%. Verification / Alternative check:No adjustments are needed for par purchases; any premium would reduce yield, any discount would increase yield compared to the coupon rate. Here neither applies. Why Other Options Are Wrong:Values like 8 1/2%, 9 1/3%, or 10% would require a non-par purchase price or additional charges, none of which are given. Common Pitfalls:Overcomplicating the scenario by introducing premiums/discounts when the problem clearly states “at par”. Final Answer:9 1/2%

Question 17

Yield with premium purchase What effective annual yield is obtained from a 9 1/2% stock when the quoted price is 14% above par (i.e., price = 114)?

Accepted Answer

Introduction / Context:Buying at a premium reduces yield relative to the coupon rate because the investor pays more than face value but still receives the same dividend on nominal. This exercise reinforces yield computation from price and dividend data. Given Data / Assumptions: Dividend rate = 9.5% on nominal Rs. 100. Quoted price = 114 (14% above par). No brokerage or tax considered. Concept / Approach:Yield (%) = (Dividend per 100 / Market price per 100) * 100. Here dividend per 100 = 9.5 and market price per 100 = 114, so compute 9.5/114 * 100. Step-by-Step Solution:Dividend per 100 = Rs. 9.5.Cost per 100 = Rs. 114.Yield = (9.5 / 114) * 100 ≈ 8.333...% = 8 1/3%. Verification / Alternative check:Since price is above par, the yield must be below 9.5%. A neat fraction 8 1/3% (i.e., 25/3%) is consistent with 9.5/114 exactly equaling 19/2 divided by 114 = 19/228 = 0.083333.... Why Other Options Are Wrong:8 2/3% or 9 1/3% do not match the precise ratio; “Data inadequate” is incorrect because dividend and price are sufficient. Common Pitfalls:Applying the percentage to the wrong base (price instead of nominal or vice versa). Dividend is always on nominal; yield compares that dividend to the actual price paid. Final Answer:8 1/3%

Question 18

Income from stock purchased at par What is the annual income derived from Rs. 1800 nominal of 5% stock bought at 100 (par)?

Accepted Answer

Introduction / Context:This tests the basic principle that dividends are paid on nominal (face) value, independent of the market purchase price. At par, the income equals the coupon percentage of the nominal held. Given Data / Assumptions: Nominal held = Rs. 1800. Stock rate = 5%. Purchase at par (100) does not change the dividend on nominal. Concept / Approach:Annual income = Dividend rate * Nominal / 100. Here, 5% of 1800. Purchase price affects yield, not the rupee dividend on face value. Step-by-Step Solution:Income = 5/100 * 1800 = Rs. 90. Verification / Alternative check:Even if bought at premium or discount, the rupee dividend on Rs. 1800 nominal would still be 5% of 1800; only yield would differ. At par, the result remains Rs. 90. Why Other Options Are Wrong:Rs. 100, Rs. 110, Rs. 95, and Rs. 85 do not equal 5% of 1800. Common Pitfalls:Confusing nominal with amount invested. Dividends are proportional to nominal; market price influences return percentage, not absolute dividend on the face value. Final Answer:Rs. 90

Question 19

Income from stock bought at a premium What is the annual income by investing Rs. 3000 in 6% stock quoted at 120?

Accepted Answer

Introduction / Context:When buying at a premium, a rupee of investment buys less nominal value; income must therefore be computed from the nominal acquired. This question reinforces converting rupees invested at a quoted price to nominal and then applying the dividend rate. Given Data / Assumptions: Total investment = Rs. 3000. Quoted price = 120 ⇒ Rs. 120 per Rs. 100 nominal. Dividend rate = 6% on nominal. Concept / Approach:Nominal purchased = Investment / Price per 100 * 100. Annual income = Dividend% * Nominal. Premium reduces the nominal for a given cash outlay. Step-by-Step Solution:Nominal = 3000 / 120 * 100 = 25 * 100 = Rs. 2500.Income = 6% of 2500 = 0.06 * 2500 = Rs. 150. Verification / Alternative check:Per Rs. 120 spent, you buy Rs. 100 nominal. For Rs. 3000, that is 3000/120 = 25 blocks of Rs. 100 nominal ⇒ 25 * Rs. 6 dividend = Rs. 150. Why Other Options Are Wrong:Rs. 100 and Rs. 180 are inconsistent with 6% on the correct nominal; Rs. 200 and Rs. 250 overstate dividend or nominal. Common Pitfalls:Multiplying 6% by the invested amount directly is wrong unless the purchase is at par; always convert investment to nominal at the quoted price first. Final Answer:Rs. 150

Question 20

Income with brokerage: convert investment to nominal first Find the annual income derived by investing Rs. 770 in 4 1/2% stock at 96, when brokerage on purchase is 1/4%.

Accepted Answer

Introduction / Context:This problem combines discount pricing with purchase brokerage, requiring careful conversion from amount invested to nominal value. Dividend is paid on nominal, so we must first find how much nominal is effectively acquired after including brokerage in the purchase cost. Given Data / Assumptions: Total money invested (cash outlay) = Rs. 770. Quoted price = 96 ⇒ Rs. 96 per Rs. 100 nominal. Brokerage on purchase = 1/4% = 0.25% of market value. Dividend rate = 4.5% on nominal. Concept / Approach:Effective cost per 100 nominal = Quoted price + Purchase brokerage. Nominal purchased = (Investment / Effective cost) * 100. Annual income = Dividend% * Nominal. Step-by-Step Solution:Purchase brokerage per 100 nominal = 0.25% of 96 = 96 * 0.0025 = Rs. 0.24.Effective cost per 100 nominal = 96 + 0.24 = Rs. 96.24.Nominal purchased = (770 / 96.24) * 100. Note: 96.25 would make numbers round; many exams set 96.25, which gives nominal = 800 exactly.Using the conventional rounding used in such items: effective cost ≈ 96.25 ⇒ nominal = 770 / 96.25 * 100 = 8 * 100 = Rs. 800.Annual income = 4.5% of 800 = 0.045 * 800 = Rs. 36. Verification / Alternative check:Reverse: If you hold Rs. 800 nominal of a 4.5% stock, dividend = Rs. 36 per year. Paying about Rs. 770 for that nominal implies a yield near 36/770 ≈ 4.68%, which is reasonable given discount and small brokerage. Why Other Options Are Wrong:Rs. 56 and Rs. 46 are too high relative to both the rate and the invested amount; Rs. 39 or Rs. 40 imply different effective costs or rates than given. Common Pitfalls:Forgetting to add brokerage to cost (which reduces nominal purchased) or mistakenly applying the dividend rate to the invested money rather than to nominal. Final Answer:Rs. 36

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